Global well-posedness for the three dimensional Muskat problem in the critical Sobolev space

Francisco Gancedo, Omar Lazar

We prove that the 3D stable Muskat problem is globally well-posed in the critical Sobolev space ${\dot{H}}^2\cap {\dot{W}}^{1,\infty }$ provided that the semi-norm $\Vert f_0 \Vert_{\dot…